Question

Let $R$ be a domain and $a,b$ $\in$ $R$, prove $R/Rb$ $\cong_R$ $Ra/Rab$

score 76 · Answer 1 · 2026-04-16 18:36:50

76

Views

Let $R$ be a domain and $a,b$ $\in$ $R$, prove $R/Rb$ $\cong_R$ $Ra/Rab$

Published on 16 Apr 2026 - 18:36

score 47 · Answer 2 · 2026-04-15 04:03:29

47

Views

Showing that $\pi(x)$ is not a prime in the ring $R=\Bbb Z[x]/I$ where $I$ is the ideal generated by $x^2+10$.

Published on 15 Apr 2026 - 4:03

score 126 · Answer 3 · 2026-03-25 19:05:05

126

Views

Prove $Ra/Rab$ $\cong_R$ $R/Rb$ , with $R$ a domain and $a,b$ not zero

Published on 25 Mar 2026 - 19:05

score 434 · Answer 4 · 2026-05-07 09:27:06

434

Views

If a finite group acts on an integral domain which is integrally closed, then the fixed point subring is also integrally closed

Published on 07 May 2026 - 9:27

score 1k · Answer 5 · 2026-04-14 18:00:25

1k

Views

Νumber of irreducible elements in $\Bbb Z_n$

Published on 14 Apr 2026 - 18:00

score 133 · Answer 6 · 2026-04-15 18:43:37

133

Views

Ideal of $(\Bbb{Z}/4\Bbb{Z})[x]/(x^2-1)$

Published on 15 Apr 2026 - 18:43

score 61 · Answer 7 · 2026-05-05 09:56:46

61

Views

Quadratic Integer Ring $\mathbb{Z}[\sqrt{-14}]$, show that $7+\sqrt{-14} \notin (7)$

Published on 05 May 2026 - 9:56

score 805 · Answer 8 · 2026-04-10 22:42:03

805

Views

Does the ring of analytic functions have zero divisors?

Published on 10 Apr 2026 - 22:42

score 240 · Answer 9 · 2026-05-05 03:07:25

240

Views

Quadratic Integer Ring $A=\mathbb{Z}[\sqrt{-14}]$, show that $7$ is irreducible in A.

Published on 05 May 2026 - 3:07

score 460 · Answer 10 · 2026-04-12 04:27:21

460

Views

Primary ideals in $\mathbb{Z}[\sqrt{-5}]$?

Published on 12 Apr 2026 - 4:27

score 102 · Answer 11 · 2026-04-15 07:10:24

102

Views

Mapping $\Bbb Z/6 \Bbb Z$ to $\Bbb F_3$ in the canonical way.

Published on 15 Apr 2026 - 7:10

score 165 · Answer 12 · 2026-04-29 15:27:49

165

Views

The quotient of an integral extension is also an integral extension

Published on 29 Apr 2026 - 15:27

score 156 · Answer 13 · 2026-04-17 22:35:22

156

Views

What is the dimension of the vector space $\mathbb Q [x]$/$((x+1)^2)$

Published on 17 Apr 2026 - 22:35

score 122 · Answer 14 · 2026-05-06 07:17:23

122

Views

Galois group of $x^5-x-1$ over $\Bbb Q$ using integral extension ring theory

Published on 06 May 2026 - 7:17

score 95 · Answer 15 · 2026-04-14 12:02:18

95

Views

Is any ring with a homomorphism out of a full matrix ring necessarily itself isomorphic to a full matrix ring?

Published on 14 Apr 2026 - 12:02

List Question

Let $R$ be a domain and $a,b$ $\in$ $R$, prove $R/Rb$ $\cong_R$ $Ra/Rab$

Showing that $\pi(x)$ is not a prime in the ring $R=\Bbb Z[x]/I$ where $I$ is the ideal generated by $x^2+10$.

Prove $Ra/Rab$ $\cong_R$ $R/Rb$ , with $R$ a domain and $a,b$ not zero

If a finite group acts on an integral domain which is integrally closed, then the fixed point subring is also integrally closed

Νumber of irreducible elements in $\Bbb Z_n$

Ideal of $(\Bbb{Z}/4\Bbb{Z})[x]/(x^2-1)$

Quadratic Integer Ring $\mathbb{Z}[\sqrt{-14}]$, show that $7+\sqrt{-14} \notin (7)$

Does the ring of analytic functions have zero divisors?

Quadratic Integer Ring $A=\mathbb{Z}[\sqrt{-14}]$, show that $7$ is irreducible in A.

Primary ideals in $\mathbb{Z}[\sqrt{-5}]$?

Mapping $\Bbb Z/6 \Bbb Z$ to $\Bbb F_3$ in the canonical way.

The quotient of an integral extension is also an integral extension

What is the dimension of the vector space $\mathbb Q [x]$/$((x+1)^2)$

Galois group of $x^5-x-1$ over $\Bbb Q$ using integral extension ring theory

Is any ring with a homomorphism out of a full matrix ring necessarily itself isomorphic to a full matrix ring?

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